Re: That or when, or another way...

: The antecedent of the relative clause is [that Grace came down.] in sentence 1, I suppose. I'm wondering why [that] is used in this sentence instead of [when]. I feel [by the time when] sounds better, but...

: 1. [The tea was cold by the time that Grace came down.]

: How about sentence 2, 3, and 4? I was told that [when] instead of [that] is not acceptable in sentence 2 while either [that] or [when] is okay in sentences 3 and 4. I really don't know why?

: 2. [It was on Monday that I bought the book.]
: 3. [It was in the morning that / when I bought the book.]
: 4. [It was Monday that / when I bought the book.]

: Thanks a lot.

: All the best,

: T. Yone

I'd refer you to The Elements of Style, which would have you throw out the lot of them, omit needless words, use the active voice, by which you would strengthen the vigor of the sentences. (Doesn't that sound like Strunk & White?) Thus:
1. The tea grew cold before Grace came down.
2. I bought the book on Monday.
3. I bought the book in the morning.
4. I bought the book Monday. Or... On Monday, I bought the book.

"When" is a good lean substitute for "by the time that" in the same way that "the fact that" is useless. I highly recommend to the whole human race the Omit Needless Words section (and sensibility) of The Elements of Style. Indispensible.